Powder Technology, 68 (1991) 235-242
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Dielectric fluid preparation by dispersing ultrafine barium titanate particles in kerosene T. Fujita Mining College, Akita University, Akira 010 (Japan)
and I. J. Lin Israel Inst. of Technology, Technion, Haifa 32000 (Israel)
(Received July 6, 1990; in revised form June 24, 1991)
Abstract Dielectric fluids whose dielectric constants depend on temperature and moisture content have been prepared by dispersing barium titanate particles in kerosene. Ultrafine barium titanate of average particle size
Introduction It is known that an external magnetic field can exert a body force on material immersed in a magnetic fluid [l]. This paper describes a method for preparing a new dielectric fluid by dispersing barium titanate particles in kerosene, and discusses the levitational forces acting on a dielectric glass sphere immersed in the fluid when an electric field gradient is applied. There are three important factors to be considered in preparing a dielectric fluid. The dispersed particles must show higher dielectric constant than the solvent, they must be ultrafine (less than a few nm), and be covered with a suitable surfactant to maintain stable dispersion in an organic solvent such as kerosene. As for the ultrafine barium titanate preparation method, Flaschen [2] and Kiss et al. [3] reported preparation of barium titanate of particle size as low as S-10 nm by hydrolysis of titanium alkoxide in barium hydroxide aqueous solution. On the other hand, Suwa ef al. [4] prepared barium titanate of m 10 nm by dropping distilled water into barium and titanium alkoxide solution. However, these particles were cubic at room temperature, as shown by X-ray diffraction, and therefore did not show ferroelectricity. Goswami [5] reported that unsintered BaTiO, did not exhibit ferroelectric properties and the decrease in dielectric constant of unsintered barium titanate with decreasing particle size below 10 pm was due to a nonferroelectric surface layer. He also showed [6] that
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the dielectric constant of explosively compacted barium titanate of tetragonal state was much lower than those of similar dense bodies obtained by conventional sintering, because of the defects in the surface layer and within the crystallites. However, the dielectric constant of barium titanate powder can be increased due to water vapor adsorbed on the surface of the particles. Goswami [5] demonstrated that the dielectric constant and dissipation factor of barium titanate powder with adsorbed water vapor varied with temperature in a non-linear fashion. Lin and Jones [7] reported the general conditions for dielectrophoretic and magnetohydrostatic levitation. The behavior of a dielectric fluid in an electric field would be expected to be analogous to that of a magnetic fluid in a magnetic field. This type of fluid is somewhat distinct from electrorheological fluids, many types of which have been prepared [8, 91 following Winslow’s first report [lo]. An electro-rheological fluid is characterized by enhanced shear strength under an electric field. Many kinds of inorganic or organic materials have been suspended in oil or water in attempts to prepare such a fluid. However, as in this case the optimum size of the dispersed solids ranges from 0.04 to 50 pm [8], it proved difficult to disperse the particles stably in the solvent, whereas the size required for a stable dielectric fluid is much smaller, namely 10-20 nm. It should also be noted that, in the presence of a water film on the particles at ambient temperature, the electric field
0 1991 - Elsevier Sequoia, Lausanne
236
causes considerable increase in viscosity by enhancing interfacial polarization in addition to its orientational counterpart. The dielectric fluid in this report is also regarded as an electro-rheological fluid under the effect of an electric field. This system of a dielectric fluid with dispersed water-free barium titanate showed no
substantial viscosity change at room temperature; however, it became a Bingham body easily at temperatures between 373 and 393 K under an electric field of sufficient strength [ll].
Experimental Preparation of barium titanate
The reagents used were as follows; 0.3 to 0.4 mol 1-l of titanium isopropoxide in isopropyl alcohol and 0.2 to 0.4 mol 1-l of barium hydroxide in boiled distilled water, or 0.3 to 0.4 mol 1-l of barium isopropoxide in isopropyl alcohol obtained by dissolving metallic barium in the alcohol at - 350 K under a nitrogen atmosphere. Titanium isopropoxide in aqueous, alkaline solutions in the presence of barium ions was hydrolyzed at several temperature levels between 313 and 353 K, yielding barium titanates. Kiss et al. [3] suggested the following reactions: Ti((CH,),CHO), +4H,O + Ba2+ + 2(OH)- Ti(OH),‘- + Ba2+ + 4(CH,),CHOH ---+ BaTiO, + 4(CH,),CHOH + 3H,O Alternatively, distilled water was added as droplets to a mixture of titanium isopropoxide at -350 K under a nitrogen atmosphere, and the barium titanate thus obtained was washed with acid to remove barium carbonate. The barium titanate prepared was analyzed as follows. The powder was heated at 1 123 K for 1 h and fused into potassium bisulfate. Barium was determined as BaSO, by gravimetric analysis, and titanium by colorimetric analysis with H,O,. Two variants of barium titanate were mainly prepared in this study, as shown in Table 1. The analytical error was 50.1% for each value. Because of the initial formation of organic carbon during heating at 1 123 K, the weight loss was large. The moisture content in particles was obtained by TABLE 1. Analytical data of barium titanate heated at 383 K for 1 h Sample No.
Mole ratio Ba:Ti
BaO (%I
TiOz (%)
Weight loss (%)
A B
19 1:1.17
60.3 56.8
31.5 34.7
8.2 8.5
measuring the weight loss after keeping the sample at 383 K in vacuum for 1 h. Three different moisture
contents were used in sample B, while sample A was completely dry. EIectric properties of powders
The conductivities of these two variants were measured with a super-megohm meter by filling them to -60% voids between concentric circle electrodes. It has been reported that compaction has no effect on resistivity in high resistance powder samples [12]; however, in electrical conductivity of powder the conductivity depends on the contact diameter between grains [13]. In our case, resistivities of well-dried particles were approximately 1Om8 S m-l. The barium titanate phases were studied by X-ray diffraction. One of the barium titanate samples, as prepared, was calcined at 1073 K in an air atmosphere in order to observe phase changes. The average particle size of barium titanate was calculated via the specific surface area determined by BET, using the density of barium titanate measured as about 5 000 kg me3 by displacing ethanol in an evacuated pycnometer. The dielectric constant of powder or fluid was measured with an LCR meter, by filling the material into the gap between concentric circle electrodes. A variety of equations are available for computing the dielectric constant of a mixture. Miller and Jones calculated the multipolar interactions of a dielectric sphere and the dielectric constant of columns and layers [14]. Paletto et al. reported the dielectric properties of powdered BaTiO, and proposed a formula for mixtures [15]. Yokoyama and Horitsu [16] reported the best agreement with experimental data when applying Lichtenecker’s equation [17] to systems of disordered mixtures with two or three nonconductive components: f(e) = WEI) + &$(G f(e) = log E
8, + 8, = 1
(Lichtenecker)
(1) (2)
where E is the dielectric constant of the mixture, e1 and e2 those of the components, and S, and 8, are the volume fractions of the components. Dispersion of powders in kerosene The surfactants used in the experiments to investigate
the dispersion of barium titanate in kerosene were sodium oleate, Duomeen TDO [R-NHCH,CH,CH,NHOCC,,H33, (molecular weight - 6OO)] and polyoxyethylene alkyl ether acetates [R-O(CH,CH,O),CH,COONa]. Sodium oleate was applied to the barium titanate in aqueous solution, and the other surfactants were added to the kerosene directly and dispersed by ultrasonic vibration or a homogenizer.
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The dispersion index was calculated by measuring the weight of particles settling out, and the state of dispersion was investigated by a transmission electron microscope (JEM 200A).
dilution in a solvent with E,* and a,, the dielectric constants of the substances are as follows, according to the Wagner theory [20].
Stability of particles in the fluid under an electric jield
A pair of well-dried ultrafine particles interacts through dipole-dipole attraction, Van der Waals attraction and steric repulsion relative to the adsorbed surfactant layer on the particle surface. Surface-charge interaction is also present, especially in the case of a moisture film under an electric field. Similar particle interaction is well known in magnetic fluids under a magnetic field [l]. The effective dipole moment P of a dielectric sphere in an imposed electrostatic field E,, in an insulating fluid is given by [18, 191.
(5)
l
where e2 and E] are the dielectric constants of dispersant and solvent, respectively, w is the frequency of the electric field, j is the electric current density. The complex relative dielectric constant of the mixture E* is
(6)
(3) where e2 and l 1 are, respectively, the relative particle and solvent dielectric constants, co the absolute dielectric constant for free space and r the particle radius. For l Z> Q, eqn. (3) reduces to P= 4w3eOe, E,. If the electric field is not too strong, the condition for a dry dielectric particle to remain stable in a fluid under a DC electric field is that the thermal energy exceeds its gravitational counterpart; i.e.:
(4) where k is the Boltzmann constant, T the temperature, so that the Brownian force is kT/r, g is the gravitational acceleration, pP the density of the particle, and pf the density of the solvent. As pi,-p,=4 000 kg rnm3, the effect of Brownian motion would exceed that of the gravitational force at less than r- 20 nm.
where r=Nr3 Lp3, L is the volume-equivalent radius of the suspension (i.e. the suspension volume is 4 rr L3/3), and N the number of particles in the solvent. Accordingly the relative dielectric constant of the mixture E is:
+ 9y[2~,+~,+3y(~,-~~>l(~~a,-~~a,)~ (2Er + E2)2(2U1 + U2)2
x 1 1+w2$ (7)
where
At w=O, with QX=-E,, Wagner theoy
Figure 1 shows the particles dispersed in the fluid. When spherical particles with complex relative dielectric constant c2* and conductivity o, are dispersed at high
9r( I + 3r)r2 E=Er(I+3Y)+ (2+ado,)2
(8)
In general, the fluid’s dielectric constant increases with increasing particle volume fraction. In our case the interfacial polarization is mainly attributed to the dielectric constant of the particles.
1*,01
‘2 Fig. 1. Model of spherical particles dispersing in a solvent.
Levitation force measurement The levitation force acting on a dielectric glass sphere
immersed in a dielectric fluid under a DC electric field was measured as shown in Fig. 2. The glass sphere was hung by a cotton fiber attached to the load cell to measure the weight change. The copper electrodes were immersed in the dielectric fluid.
238
I
DC power SUPPlY
t-Cotton fiber
Dielectric Copper plate (0.5mm thickness)
k---Cubic system 01 BaTiO3 by x-ray ’ diffraction 1 I 333 373 Reaction temperature, K
Glass sphere
293
Fig. 3. Effect of reaction temperature on particle size and crystal structure of coprecipitated barium titanate. Initial mole ratio by coprecipitation Ba:Ti = 1:l. Fig. 2. Cross-section of a glass sphere immersed in dielectric fluid, to measure the levitation force in an applied electric field.
Results and discussion
Heated at 1073K for Sminutes
Jl-,__A__n_
Preparation of barium titanate
Different sizes of barium titanates were prepared by hydrolysis of titanium isopropoxide in aqueous alkaline solutions in the presence of barium ions at several temperatures, as shown in Fig. 3. The average particle size was -5-20 nm and the particle size decreased as reaction temperature decreased. The barium titanate prepared above 330 K showed a cubic system. The particles prepared at -350 K using titanium isopropoxide and barium hydroxide or barium isopropoxide were -20 nm in size. The barium:titanium mole ratio was 1:l. X-ray diffraction patterns of the barium titanate, as prepared and after heating for 5 min at 1073 K, are shown in Fig. 4. As-prepared, the barium titanate was cubic and thus did not show ferroelectricity. On heating, the cubic system changed into a tetragonal one. However, the dielectric constant of the calcined barium titanate powder was little greater than that of the material as prepared, because the nonferroelectric surface layer was high in ultrafine particles (as Goswami reported [5]), and its particle size was too large (80 nm) to disperse stably in kerosene. Next, barium titanate with a molar ratio of titanium to barium greater than unity was prepared at -320 K. These particles were amorphous, as shown by X-ray diffraction, and the average particle size was 5-10 nm. The dielectric constants of the particles with
Tetragonal system of BaTi
(a)
Cubic system 0T UaTiO As prepared
3
JL___I\ II
(b)
1
I
I
30 20
I
40 (Cu Ka),
50 deg
Fig. 4. X-ray diffraction patterns of (a) heated and (b) asprepared barium titanate. Composition: sample A, coprecipitated at -350 K.
and without moisture are compared in Fig. 5. The volume percentage of the powder was -35 in this dielectric constant measurement. The dielectric constant of the particles with no moisture depended little on frequency. When the particles contained moisture, the dielectric constant of particles of Ba:Ti mole ratio 1:1.17 was a little higher than that of equirnolar proportions of Ba and Ti. It seems that the crystal structure was distorted by the increased proportion of the titanium ion. For particles with moisture, the dielectric constant was higher at lower frequency and higher moisture content. The dielectric loss
239
E
10 I_
o1o2
,
III
I
I
I
II
Frequency,
I 104
103
I
III
1 105
Hz
Fig. 5. Effects of frequency and moisture content on relative dielectric constant of barium titanate powder (35 vol.%) measured at 293 K and 1 kHz, coprecipitated at -320 K. Sample A, moisture content 0 (wt.%) (A); sample B, moisture content 0 (wt.%) (o), 4.3 ((D), 6.8 (a). 1.2
r
0
0.2 Volume
0.4
0.6
fraction of barium titanate, -
Fig. 7. Effect of voiume fraction on relative dielectric constant of barium titanate powder with no moisture. Composition: sample B, coprecipitated at -320 K, measured at 293 K and 1 kHz (0), 10 kHz (A). 25 r
Frequency,
Hz
Fig. 6. Effects of frequency and moisture content on dielectric loss tangent of barium titanate powder (35 vol.%) measured at 293 K and 1 kHz, coprecipitated at -320 K. Symbols as in Fig. 5.
tangent (shown in Fig. 6) increased with decreasing frequency, especially at higher moisture. Figure 7 shows the dependence of the dielectric constant on the volume fraction of barium titanate with no moisture. The dielectric constant agreed well with the Lichtenecker eqn. (2). From Fig. 7, the dielectric constant of ultrafine barium titanate of Ba:Ti mole ratio 1:1.17 was -30 at 1 kHz. The effect of temperature on the dielectric constant of particles with moisture is shown in Fig. 8. At the beginning of the heating stage, the dielectric constant with moisture increased to 24 for 35% solids by volume at 363 K and 1 kHz, and then decreased with further increase in temperature. At the cooling stage the dielectric constant became low, decreased gradually and showed no peak between 293 and 393 K This cooling curve of dielectric constant was similar to that of particles with no moisture.
0
I 293
I
333
I
373
I
393
Temperature, K
Fig. 8. Effect of temperature on relative dielectric constant of barium titanate powder with moisture initially heated and then cooled (35 vol.%). Composition: sample B, coprecipitated at -320 K, measured at 1 kHz, moisture content 4.3 wt.%.
Preparation of dielectric @id
As-prepared barium titanate (Ba:Ti = 1:1.17) with average size N 8 nm was employed to investigate the dispersion condition in kerosene. Oleate-coated barium titanate did not disperse in kerosene, even on addition of Duomeen TDO. Addition of polyoxyethylene alkyl ether acetates led to satisfactory dispersion. Figure 9 shows the effect on dispersion of concentration of the specific surfactant sodium POE(6) alkyl ether acetate. Approximately 100 kg mm3 of surfactant was needed
240
O&H 0
I
40
1
I
I
80
120
160 1
Added. amount of surfactant, kg/m3 Fig. 9. Effect of added amount of surfactant on dispersion of barium titanate, after dispersion for 1 min by ultrasonic vibration and centrifugation at - lo4 g for 5 min. Composition: sample B, coprecipitated at -320 K, surfactant: sodium POE(6) alkyl ether acetate, initial concentration o f b a r i u m titanate: 100 kg me3, solvent: kerosene, average particle size: 8 nm.
293
333
1
373
I 393
'Temperature, K Fig. 11. Effect of temperature on relative dielectric constant of dielectric fluids with dispersed barium titanate, with and without moisture. Composition: sample B, coprecipitated at -320 K, measured at 1 kHz, 12.6 wt.% barium titanate powder in kerosene, moisture content 4.3 wt.% (0), 0 wt.% (0).
at 353 K, and was -9.5 at 373 K. The temperature corresponding to the highest dielectric constant in the fluid differed from that of the powder. At higher frequencies, the dielectric constant decreased and showed no peak at 100 kHz. This phenomenon was related to the moisture around the particle surface. The fluid conductivity was about 10e6 S m-’ at 293 K. The boiled dielectric fluid which had no moisture did not show the increase described above. Measurement of levitation force
Fig. 10. TEM micrograeh of barium titanate dispersed in kerosene. Composition: sample B coprecipitated at -320 K, moisture content 0 wt.%.
to disperse 100 kg me3 of barium titanate, and the dispersion percentage was 65%. A transmission electron micrograph is shown in Fig. 10. To observe the dispersion effect, the fluid as prepared was diluted to a volume percentage less than 0.1. This diluted fluid was put onto a 100 mesh copper sieve coated with collodion film, and dried in a desiccator. Ultrafine particles were seen to be well dispersed in kerosene. Figure 11 shows the effect of temperature on the dielectric constant of a dielectric fluid with 12.6 wt.% of barium titanate (Ba:Ti=1:1.17) with and without moisture in kerosene. At 1 kHz the dielectric constant of a dielectric fluid with moisture suddenly increased
Using the equipment in Fig. 2, the levitation force acting on a glass sphere in the dielectric fluid was measured. The dielectric levitation force in the insulating case is given by Lin and Jones [7] as follows. F = 271.R3e04
VEo2
Here Ed and cP are the relative dielectric constants of the fluid and the object respectively, EO is the imposed electric field, and R the radius of the glass sphere. For the experiments with a glass sphere, eP=2.5 at 1 kHz and R = 5 mm. For R -KX, the force F’ per unit volume of the sphere is given by Andres [21] as:
(10) Figure 12 shows the levitation force acting on a glass sphere immersed in a’ dielectric fluid under an electric field. Dielectric fluids of two different dielectric constants dispersing almost water-free particles were em-
241
disperse barium titanate and Prof. M. Mamiya, Akita University and Mr. S. Kooriyama, Tokyo Electron, Tokyo, for helping with preparation of the barium titanate. The valuable suggestions of the reviewers are highly appreciated. Financial support from the Education Ministry of Japan [Grant-in-Aid 1991 (03650514)] is gratefully acknowledged. List of symbols &I
0
2 4 Electric field, V/m
6x10'
Fig. 12. Levitation force acting on a glass sphere immersed in a dielectric fluid under electric field gradient. Measured at 293 K, x in Fig. 2=25 mm, relative dielectric constant of fluid: 3.5 (0), 2.9 (0).
ployed at 293 K. The equipment shown in Fig. 2 was employed and the distancex, between the glass sphere and the bottom, was 25 mm. The levitation force per unit volume increased in proportion to the square of the electric field intensity, as expected from eqn. (10). On the other hand, when the dielectric fluid with moisture shown in Fig. 11 was used at the fluid temperature 363 K, the barium titanate particles accumulated at the negative electrode when the applied electric field exceeded 1 X 105 V m-l. Therefore, the levitation force could not be measured. Conclusion
Amorphous barium titanate has been prepared by hydrolysis of titanium isopropoxide in aqueous alkaline solutions in the presence of barium ions at -320 K. The dielectric constant of the barium titanate is strongly dependent on the moisture content. As the average particle size was in the range 5-10 nm, the particles dispersed stably in kerosene when coated with surfactant polyoxyethylene alkyl ether acetates. A glass sphere immersed in the resulting dielectric fluid with low moisture content experienced a levitation force under the influence of an electric field gradient. Acknowledgement The authors wish to thank Dr. K. Kawata, Taiho Industries, Tokyo, for investigating the surfactant to
F F’ g i k L N P R r T V x
electric field levitation force levitation force per unit volume gravitational acceleration electric current density Boltzmann constant radius of solvent dispersing particles number of particles in the solvent dipole moment glass sphere radius particle radius temperature voltage vertical distance to the glass sphere
Greek letters angle between copper poles volume fraction of spherical particles in a fluid volume ratio of component 1 (fluid) volume ratio of component 2 (particle) relative dielectric constant of a mixture absolute dielectric constant for free space relative dielectric constant of component 1 (fluid) relative dielectric constant of component 2 (particle) relative dielectric constant of dielectric fluid relative dielectric constant of object (glass) complex relative dielectric constant of a mixture complex relative dielectric constant of a fluid complex relative dielectric constant of a particle density of fluid density of particle conductivity of fluid conductivity of particle relaxation time frequency of the electric field References 1 R. E. Rosensweig, Ferrohydroynamics, Cambridge University Press, New York, 1985, p. 124. 2 S. S. Flaschen, J. Am. Chem. SM., 77 (1955) 6194. 3 K Kiss, J. Magder, M. S. Vukasovich and R. J. Lockhart, J. Am. Ceram Sot., 49 (1966) 291.
242 4 Y. Suwa, Y. Sugimoto and S. Naka, J. Jpn. Sot. Powder, Powder Metall., 25 (1978) 164. A. K. Goswami, J. Appl Phys., 40 ( 1 9 6 9 ) 6 1 9 . A. K. Goswami, J. Am. Ceram. Sot., 56 (1973) 100. 1. J. Lin and T. B. Jones, J. Electrosta/ics, 15 (1984) 53. H. Block and J. P. Kelly, J. PhysB, Appl. Phys., 21 (1988) 1661. 9 H. Block, J. P. Kelly, A. Qin and T. Watson, Langmuir, 6 (1990) 6. 10 U.S. Pat. 2417850 (1947) to W. M. Winslow. 11 T. Fujita, I. J. Lin and M. Mamiya, I’roc. 2nd ISEM Meeting, Inr. Symp. Appl. Electromagn. Forces, Sendai, Japan, 1991. 12 S. Mugeraya and B. R. Prabhakar, J. Electrosratics, 18 (1986) 109.
13 K. Kendall, Powder Technol., 62 (1990) 147. 14 R. D. Miller and T. B. Jones, J. Phys.D, Appl. Phys., 21 (1988) 527. 15 J. Paletto, R. Grange, R. Goutte and L. Eyraud, Chim. Mod., 11 (1966) 201. 16 H. Yokoyama and T. Horitsu, J. Mining Metall. Inst. Jpn., 9 4 (1978) 317. 17 K. Lichtenecker, Z. Phys., 25 (1924) 169. 18 A. R. Von Hippel, Dielectrics and Waves, Wiley, New York, 1954, p. 39. 19 L. Benguigui and I. J. Lin, J. Appl. Phys., 53 (1982) 1141. 20 The Institute of Electrical Engineers of Japan, Dielecttic Phenomena, Ohmu-sha, Tokyo, 1973, p. 145. 21 U. T. Andres, in R. J. Wakeman (ed.), Progress in Filrration and Separation, Vol. II, Elsevier, Amsterdam, 1981, p. 125,